An effective model to decompose linear programs for parallel solution
Date
1996-08Source Title
Applied Parallel Computing Industrial Computation and Optimization
Third International Workshop, PARA '96
Print ISSN
0302-9743
Publisher
Springer
Pages
592 - 601
Language
English
Type
Conference PaperItem Usage Stats
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Abstract
Although inherent parallelism in the solution of block angulax Linear Programming (LP) problems has been exploited in many research works, the literature that addresses decomposing constraint matrices into block angular form for parallel solution is very rare and recent. We have previously proposed hypergraph models, which reduced the problem to the hypergraph partitioning problem. However, the quality of the results reported were limited due to the hypergraph partitioning tools we have used. Very recently, multilevel graph partitioning heuristics have been proposed leading to very successful graph partitioning tools; Chaco and Metis. In this paper, we propose an effective graph model to decompose matrices into block angular form, which reduces the problem to the well-known graph partitioning by vertex separator problem. We have experimented the validity of our proposed model with various LP problems selected from NETLIB and other sources. The results are very attractive both in terms of solution quality and running times. © Springer-Verlag Berlin Heidelberg 1996.
Keywords
Linear programmingMatrix algebra
Optimization
Graph partitioning
Graph partitioning by vertex separators
Hypergraph model
Hypergraph partitioning
Inherent parallelism
Multilevel graph partitioning
Parallel solutions
Solution quality
Graph theory